Presupposition, An inference that survives the Projection Test, meaning the background assumption remains true even if the main sentence is negated., Proposition, The set of all possible worlds in which a specific sentence is true., Beta Reduction, A formal, mechanical procedure where you delete the lambda head (λx) and replace every occurrence of that variable in the body with a specific argument., Functional Application (FA), The core semantic "ur-rule" where a function of type ⟨σ,τ⟩ combines with an argument of type σ to yield an output of type τ., Tautology, A sentence that is true in every possible world, meaning its proposition equals the entire logical space (W)., Entailment, An inference that does not project under negation and corresponds to subsethood in set theory (e.g., if one is a reggaeton artist, they are an artist)., Characteristic Function, A mapping that assigns a truth value of 1 if an individual is in a set, and 0 if they are not, serving as a uniform format for one-place predicates., Principle of Compositionality, The idea that complex meanings are calculated strictly from the meanings of their individual parts and their syntactic structure., Semantic Type e, The basic semantic type that stands for concrete entities or specific individuals (e.g., John, Mary, Shakira)., Relation, A mathematical set consisting entirely of ordered pairs., Function, A specific type of relation following the "no two-timing" rule, where each element in the domain maps to at most one unique element in the codomain., Semantic Type t, The basic semantic type that represents truth values, which evaluate to exactly 1 (True) or 0 (False)., Cancellation Test, A diagnostic tool used to determine if a meaning is an entailment; if adding "but not X" creates a contradiction, the meaning is hard-wired and cannot be removed., Semantic Type ⟨e,t⟩, The semantic type representing a function that takes an entity (e) as an input and returns a truth value (t) as an output, typically used for intransitive verbs like smiled or dances., Semantic Equivalence, A relationship between two propositions where they mutually entail each other, meaning they express the exact same set of possible worlds., Strict Contradictories, Two propositions that are completely disjoint and exhaust the entire logical space, meaning they can never both be true or both be false at the same time., Implicature , An implied meaning (such as interpreting "or" as "not both") that is suggested by the speaker based on conversational rules, but is not strictly built into the literal meaning., Extension, The actual, real-world referent of an expression at a specific world, such as a specific individual for a proper name, or a set of individuals for a predicate., Projection Test, A diagnostic tool that involves embedding a sentence under negation to see if an underlying inference survives; if it does not survive, the inference is merely an entailment, not a presupposition., Contrariety , A semantic relationship between two propositions where they cannot both be true at the same time, but they can both be false (e.g., "The coffee is freezing cold" and "The coffee is boiling hot")..

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